Simplify (2z+5)^2-(z-3)^2

${(2 z + 5)}^{2} - {(z - 3)}^{2}$

Step 1

Simplify each term.

Rewrite

${(2 z + 5)}^{2}$ as

$(2 z + 5) (2 z + 5)$ .

$(2 z + 5) (2 z + 5) - {(z - 3)}^{2}$

Expand

$(2 z + 5) (2 z + 5)$ using the FOIL Method.

Apply the distributive property.

$2 z (2 z + 5) + 5 (2 z + 5) - {(z - 3)}^{2}$

Apply the distributive property.

$2 z (2 z) + 2 z \cdot 5 + 5 (2 z + 5) - {(z - 3)}^{2}$

Apply the distributive property.

$2 z (2 z) + 2 z \cdot 5 + 5 (2 z) + 5 \cdot 5 - {(z - 3)}^{2}$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 z \cdot z + 2 z \cdot 5 + 5 (2 z) + 5 \cdot 5 - {(z - 3)}^{2}$

Multiply

$z$ by

$z$ by adding the exponents.

Move

$z$ .

$2 \cdot 2 (z \cdot z) + 2 z \cdot 5 + 5 (2 z) + 5 \cdot 5 - {(z - 3)}^{2}$

Multiply

$z$ by

$z$ .

$2 \cdot 2 z^{2} + 2 z \cdot 5 + 5 (2 z) + 5 \cdot 5 - {(z - 3)}^{2}$

Multiply

$2$ by

$2$ .

$4 z^{2} + 2 z \cdot 5 + 5 (2 z) + 5 \cdot 5 - {(z - 3)}^{2}$

Multiply

$5$ by

$2$ .

$4 z^{2} + 10 z + 5 (2 z) + 5 \cdot 5 - {(z - 3)}^{2}$

Multiply

$2$ by

$5$ .

$4 z^{2} + 10 z + 10 z + 5 \cdot 5 - {(z - 3)}^{2}$

Multiply

$5$ by

$5$ .

$4 z^{2} + 10 z + 10 z + 25 - {(z - 3)}^{2}$

Add

$10 z$ and

$10 z$ .

$4 z^{2} + 20 z + 25 - {(z - 3)}^{2}$

Rewrite

${(z - 3)}^{2}$ as

$(z - 3) (z - 3)$ .

$4 z^{2} + 20 z + 25 - ((z - 3) (z - 3))$

Expand

$(z - 3) (z - 3)$ using the FOIL Method.

Apply the distributive property.

$4 z^{2} + 20 z + 25 - (z (z - 3) - 3 (z - 3))$

Apply the distributive property.

$4 z^{2} + 20 z + 25 - (z \cdot z + z \cdot - 3 - 3 (z - 3))$

Apply the distributive property.

$4 z^{2} + 20 z + 25 - (z \cdot z + z \cdot - 3 - 3 z - 3 \cdot - 3)$

Simplify and combine like terms.

Simplify each term.

Multiply

$z$ by

$z$ .

$4 z^{2} + 20 z + 25 - (z^{2} + z \cdot - 3 - 3 z - 3 \cdot - 3)$

Move

$- 3$ to the left of

$z$ .

$4 z^{2} + 20 z + 25 - (z^{2} - 3 \cdot z - 3 z - 3 \cdot - 3)$

Multiply

$- 3$ by

$- 3$ .

$4 z^{2} + 20 z + 25 - (z^{2} - 3 z - 3 z + 9)$

Subtract

$3 z$ from

$- 3 z$ .

$4 z^{2} + 20 z + 25 - (z^{2} - 6 z + 9)$

Apply the distributive property.

$4 z^{2} + 20 z + 25 - z^{2} - (- 6 z) - 1 \cdot 9$

Simplify.

Multiply

$- 6$ by

$- 1$ .

$4 z^{2} + 20 z + 25 - z^{2} + 6 z - 1 \cdot 9$

Multiply

$- 1$ by

$9$ .

$4 z^{2} + 20 z + 25 - z^{2} + 6 z - 9$

Step 2

Simplify by adding terms.

Subtract

$z^{2}$ from

$4 z^{2}$ .

$3 z^{2} + 20 z + 25 + 6 z - 9$

Add

$20 z$ and

$6 z$ .

$3 z^{2} + 26 z + 25 - 9$

Subtract

$9$ from

$25$ .

$3 z^{2} + 26 z + 16$

Simplify (2z+5)^2-(z-3)^2

Related Questions